hpev(3)

NAME
hpev - {hp,sp}ev: eig, QR iteration

SYNOPSIS

  Functions
subroutine chpev (jobz, uplo, n, ap, w, z, ldz, work, rwork, info)
CHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine dspev (jobz, uplo, n, ap, w, z, ldz, work, info)
DSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine sspev (jobz, uplo, n, ap, w, z, ldz, work, info)
SSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine zhpev (jobz, uplo, n, ap, w, z, ldz, work, rwork, info)
ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Detailed Description

Function Documentation

  subroutine chpev (character jobz, character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, real, dimension( * ) rwork, integer info)

CHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> CHPEV computes all the eigenvalues and, optionally, eigenvectors of a
    !> complex Hermitian matrix in packed storage.
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only;
    !>          = 'V':  Compute eigenvalues and eigenvectors.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, AP is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    !>          and first superdiagonal of the tridiagonal matrix T overwrite
    !>          the corresponding elements of A, and if UPLO = 'L', the
    !>          diagonal and first subdiagonal of T overwrite the
    !>          corresponding elements of A.
    !>

    W

    !>          W is REAL array, dimension (N)
    !>          If INFO = 0, the eigenvalues in ascending order.
    !>

    Z

    !>          Z is COMPLEX array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(i).
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension (max(1, 2*N-1))
    !>

    RWORK

    !>          RWORK is REAL array, dimension (max(1, 3*N-2))
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the algorithm failed to converge; i
    !>                off-diagonal elements of an intermediate tridiagonal
    !>                form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 136 of file chpev.f.

  subroutine dspev (character jobz, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer info)

DSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> DSPEV computes all the eigenvalues and, optionally, eigenvectors of a
    !> real symmetric matrix A in packed storage.
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only;
    !>          = 'V':  Compute eigenvalues and eigenvectors.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the symmetric matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, AP is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    !>          and first superdiagonal of the tridiagonal matrix T overwrite
    !>          the corresponding elements of A, and if UPLO = 'L', the
    !>          diagonal and first subdiagonal of T overwrite the
    !>          corresponding elements of A.
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0, the eigenvalues in ascending order.
    !>

    Z

    !>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(i).
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension (3*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the algorithm failed to converge; i
    !>                off-diagonal elements of an intermediate tridiagonal
    !>                form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 129 of file dspev.f.

  subroutine sspev (character jobz, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info)

SSPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> SSPEV computes all the eigenvalues and, optionally, eigenvectors of a
    !> real symmetric matrix A in packed storage.
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only;
    !>          = 'V':  Compute eigenvalues and eigenvectors.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    AP

    !>          AP is REAL array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the symmetric matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, AP is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    !>          and first superdiagonal of the tridiagonal matrix T overwrite
    !>          the corresponding elements of A, and if UPLO = 'L', the
    !>          diagonal and first subdiagonal of T overwrite the
    !>          corresponding elements of A.
    !>

    W

    !>          W is REAL array, dimension (N)
    !>          If INFO = 0, the eigenvalues in ascending order.
    !>

    Z

    !>          Z is REAL array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(i).
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is REAL array, dimension (3*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the algorithm failed to converge; i
    !>                off-diagonal elements of an intermediate tridiagonal
    !>                form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 129 of file sspev.f.

  subroutine zhpev (character jobz, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info)

ZHPEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
    !> complex Hermitian matrix in packed storage.
    !>

Parameters
    JOBZ

    !>          JOBZ is CHARACTER*1
    !>          = 'N':  Compute eigenvalues only;
    !>          = 'V':  Compute eigenvalues and eigenvectors.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          = 'U':  Upper triangle of A is stored;
    !>          = 'L':  Lower triangle of A is stored.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          On entry, the upper or lower triangle of the Hermitian matrix
    !>          A, packed columnwise in a linear array.  The j-th column of A
    !>          is stored in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
    !>
    !>          On exit, AP is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the diagonal
    !>          and first superdiagonal of the tridiagonal matrix T overwrite
    !>          the corresponding elements of A, and if UPLO = 'L', the
    !>          diagonal and first subdiagonal of T overwrite the
    !>          corresponding elements of A.
    !>

    W

    !>          W is DOUBLE PRECISION array, dimension (N)
    !>          If INFO = 0, the eigenvalues in ascending order.
    !>

    Z

    !>          Z is COMPLEX*16 array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(i).
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (max(1, 2*N-1))
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit.
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the algorithm failed to converge; i
    !>                off-diagonal elements of an intermediate tridiagonal
    !>                form did not converge to zero.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 136 of file zhpev.f.

Author

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